Random reboots and crashes

Hey guys, thought I might put my current dilemma with the iPhone 5 and iOS 7. I got an iPhone 5 last June as a gift from a friend (upgraded from a 4S), I was supposed to wait for the 5S, but since I got this one as a gift I thought I'll just keep and wait for the next one after the 5S. Once I got it I already preloaded iOS 7 Beta 4 and everything worked well for about 3 months up until iOS 7.0.1. After I have installed iOS 7.0.2, that's when random stuff started happening. Here are a few:

- Random reboots while using the phone, any app or even on standby.
- One reboot took a while before it restarted and after showing the Apple logo, it went to DFU mode asking me to plug it in to iTunes (had to restore and good thing I had a backup)
- Normally random reboots will just show the screen turn blank and then restart. However in my case, the screen would show various lines and would somehow mess up the display and then it would restart.
- After rebooting my iPhone will be stuck at 'Searching...' when looking for a phone signal, and I had to reset the phone again to get back a signal.

Like every other user I have restored several times, and even restored from scratch (clean install without any backups). It will work fine for some days but then the problem will come back.

I'm starting to think it might be a defective unit. Thing is, my friend got from the US, it's a Verizon iPhone 5 (saw the SIM card when I opened it) and I'm based here in the UAE so having it checked out will be a problem.

I can simply purchase a new one if it comes to that, but yeah I want to exhaust all the possible solutions before I do that. Just checking if anyone encountered the same situation, let me know what you think.